SBL-based multi-task algorithms for recovering block-sparse signals with unknown partitions
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SBL-based multi-task algorithms for recovering block-sparse signals with unknown partitions Ying-Gui Wang1* , Le Yang1,2 , Zheng Liu1 and Wen-Li Jiang1
Abstract We consider in this paper the problem of reconstructing block-sparse signals with unknown block partitions. In the first part of this work, we extend the block-sparse Bayesian learning (BSBL) originally developed for recovering a single block-sparse signal in a single compressive sensing (CS) task scenario to the case of multiple CS tasks. A new multi-task signal recovery algorithm, called the extended multi-task block-sparse Bayesian learning (EMBSBL), is proposed. EMBSBL exploits the statistical correlation among multiple signals as well as the intra-block correlation within individual signals to improve performance. Besides, it does not need a priori information on block partition. As the second part of this paper, we develop the EMBSBL-based synthesized multi-task signal recovery algorithm, namely SEMBSBL, to make it applicable to the single CS task case. The idea is to synthesize new CS tasks from the single CS task via circular-shifting operations and utilizes the minimum description length principle to determine the proper set of the synthesized CS tasks for signal reconstruction. SEMBSBL can achieve better signal reconstruction performance over other algorithms that recover block-sparse signals individually. Simulations corroborate the theoretical developments. Keywords: Sparse Bayesian learning; Block-sparse; Multi-task; Circular shifting; Minimum description length
1 Introduction Compressive sensing (CS) enables reconstructing a signal that is sparse in a certain domain from its measurements obtained at a rate significantly lower than the Nyquist frequency [1]. If in addition to sparsity, the signal representation is also structured in the form of clustered non-zeros, the signal would be referred to as being block-sparse. In practice, block-sparsity can be found in multi-band signals [2] or in the measurements of gene expression levels [3]. It has been shown that exploring the block-sparsity enables robust signal recovery from fewer compressive measurements [4]. We shall consider in this paper the efficient recovery of block-sparse signals. Several block-sparse signal reconstruction algorithms have been developed in literature. Based on the compressive sampling matching pursuit (CoSaMP) [5], the block compressive sampling matching pursuit (BCoSaMP) was proposed in [4]. It utilizes the knowledge on the number of non-zero blocks to achieve signal recovery. On the basis of the orthogonal matching pursuit (OMP) [6], the block *Correspondence: [email protected] 1 College of Electronic Science and Engineering, National University of Defense Technology, Deya Road, Changsha 410073, People’s Republic of China Full list of author information is available at the end of the article
orthogonal matching pursuit (BOMP) was developed in [7]. Zou et al. proposed a block fixed-point continuation algorithm in [8] for block-sparse signal re
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